Shouldn't it be यह rather than ये, as mother is singular?
ये is used here to show respect.
And is that why it is not है but हैं ?
Yes. 1st person हम and (in this example) 3rd person ये/वे/आप use हैं. In Hinglish, you'd type है like "hai" and हैं like "hain" to make it clear for anyone reading.
In formal situations and for respected people (including all elders), plural versions are used in every context.
Why 'meri' instead of 'mere'?
Mother is female, and the plural form of feminine adjectives gives merī, not mere (which is for masculine plural nouns).